ГДЗ по алгебре 9 класс Макарычев Задание 891

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\[x_{2} = - 32,\ \ q = - \frac{1}{2},\ \ \]

\[S_{10} = ?\]

\[x_{2} = x_{1} \cdot q,\ \]

\[x_{1} = \frac{x_{2}}{q} = 32 \cdot 2 = 64,\]

\[S_{10} = \frac{x_{1} \cdot \left( q^{10} - 1 \right)}{q - 1} =\]

\[= \frac{64 \cdot \left( \left( - \frac{1}{2} \right)^{10} - 1 \right)}{- \frac{1}{2} - 1\ } =\]

\[= \frac{64 \cdot 1023}{1024} \cdot \frac{2}{3} = \frac{341}{8} = 42\frac{5}{8}.\]